In Minkowski space, the covariant derivative can be chosen to coincide with a partial one, \({\cal D}_a = \delta _a{}^m \partial _m = \partial _a\) . Then one can derive the following closed-form expression for the higher-spin Cotton tensorRelation (REF ) was obtained
in [1]} via the component reduction of the higher-spin \({\cal N}=1\)  super-Cotton tensor, eq. (REF ), which is remarkably simple. This is an example of the power of supersymmetry.
[1]}
\({\mathfrak {C}}_{\alpha (n)}(h)&:=\frac{1}{2^{n-1}} \sum \limits _{j=0}^{ \lceil {n/2} \rceil -1 }\binom{n}{2j+1}\Box ^{j}\big (\partial _{\alpha }{}^{\beta }\big )^{n-2j-1}h_{\alpha (2j+1)\beta (n-2j-1) }~.\) 
